WASHINGTON (CNN) -- Days after he officially jumped into the Republican race for the White House, former Tennessee Sen. Fred Thompson finds himself in a statistical dead heat with Rudy Giuliani, according to a CNN/Opinion Research Corp. poll released Tuesday.

Fred Thompson announces his presidential candidacy on "The Tonight Show" with Jay Leno last week.

The former New York mayor garners 28 percent nationally among registered Republicans, while Thompson is one point behind at 27 percent -- well within the poll's 5 percentage point margin of error.

In a similar poll taken in August, Giuliani registered 29 percent, while Thompson, then not an official candidate, was at 22 percent.

CNN senior political analyst Bill Schneider said, "Thompson has the edge among evangelical Republicans and especially among his fellow southerners; that's where Thompson has made the biggest gains."

Specifically, Thompson leads among men, southerners, voters age 50 and older and ideological conservatives. Conversely, Giuliani leads among women, voters in the Northeast and Midwest, voters under 50 and self-described GOP moderates.

While the CNN/Opinion Research Corp. Poll shows a statistical dead heat, other recent national polls indicate Giuliani continues to hold a lead over Thompson. A CBS/New York Times poll released Monday showed Giuliani with a 5 point lead over Thompson, 27 percent to 22 percent. Meanwhile, a USAToday/Gallup poll out Monday had Giuliani with a 12 point lead, 34 percent to 22 percent.

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Arizona Sen. John McCain comes in third at 15 percent, with former Massachusetts Gov. Mitt Romney close behind at 11 percent. McCain was at 16 percent in the August poll, while Romney registered 12 percent. Former Arkansas Gov. Mike Huckabee is at 5 percent, while no other Republican candidate pulls more than 2 percent.

The poll surveyed 318 registered Republicans from September 7-9.

Despite Thompson's entry into the race Wednesday night, 25 percent of registered Republicans polled said they are not satisfied with the GOP candidates -- virtually the same percentage (26 percent) who were not satisfied in May.

The poll also suggests Democratic front-runner Sen. Hillary Clinton would beat Thompson in a general election by 13 percentage points, 55 percent to 42 percent.

When CNN and the Opinion Research Corp. asked the same question in June, the New York senator edged out Thompson by 4 percentage points, 50 percent to 46 percent.

When paired with Giuliani, Clinton comes out on top by four percentage points, 50 percent to 46 percent. Clinton was ahead by 1 percent in the same matchup in June, 49 percent to 48 percent.

Meanwhile, Sen. Barack Obama also beats Thompson head to head, 53 percent to 41 percent. In June, the Illinois Democrat led Thompson by the same margin, 52 percent to 40 percent.

According to Schneider, "The main reason Giuliani does better than Thompson [in head-to-head matchups] is that he's better known. Forty-seven percent of the public say they have never heard of Fred Thompson or have an opinion of him. Only 14 percent have no opinion of Rudy Giuliani."

For the questions on hypothetical matchups 1,017 adults were surveyed on September 7-9. Those questions carry a margin of error of 3 percentage points.E-mail to a friend